A senior backbench Fianna Fáil TD has said "now is not the time for a change in leadership" in the party.
Speaking on RTÉ's Today with Claire Byrne, Jim O'Callaghan said Taoiseach Micheál Martin has his "full support".
He said he will not "be seen to undermine the Taoiseach" by discussing his own leadership aspirations.
Earlier this week, his party colleague Éamon Ó Cuív said Fianna Fáil needs a new leader and a "change of direction".
Mr Ó Cuív said that Fianna Fáil was in danger of disappearing and it had lost touch with its support base in recent times.
This morning Mr O'Callaghan said he has not been approached by any party colleague to "push Micheál Martin out".
However he said he would be honoured to lead the party.
"It would be an honour for any member of Fianna Fáil to lead the party. I can't predict the future. I'm certainly not going to say I'm not interested.
"When there is a vacancy for leadership I will give it consideration, and if party colleagues want to nominate me I certainly will do that."
Mr O'Callaghan commended the Government's plan for Living with Covid-19.
"The plan in itself is very good. It is very detailed. We can't have some very simply three word document when we are trying to deal with a pandemic while trying to account for social, economic and health factors."
He said the guidance in relation to restrictions in Dublin was clear, and people should not "look at this plan with a view to catching out politicians".
The senior backbencher said he does not regret passing up the job of a junior minister, because he said he has been proved correct in his belief that it is a "limited role".
"It is my responsibility as a senior backbench TD for Fianna Fáil who is not in Government to get out there and support the other members of the party at this time," he said.
The Dublin Bay South TD said that ratings in an opinion poll last weekend were "disappointing", and that the party needs to "protect and emphasise its identity".
He said "for the interest of Ireland" the Fianna Fáil party "has to survive".
"We are centre ground, centre left national party, that wants to reunify the country, build public housing, reward hard work, protect the vulnerable, the Irish language and save our environment."
He said if the party does not survive, Ireland will have a political system similar to that of the US, the UK and Northern Ireland.